All categories

4 years ago

Find the number of sides of the regular polygon when the measure of an exterior angle is given.

1 answer:

8 0

$1.\\exterior\angle=30^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -30^\circ=150^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 150^\circ=180^\circ-\frac{360^\circ}{n}\\ -30^\circ=-\frac{360^\circ}{n}\ |*n\\ -30^\circ\ *n=-360^\circ \ |:-30^\circ\\ n=12\\\\ Number\ of\ sides\ is\ 12.$ $2.\\exterior\angle=10^\circ\\ exterior\angle=180^\circ-interior\ angle\\ interior\angle=180^\circ-exterior\ angle=180^\circ -10^\circ=170^\circ\\ \\Formula\ for\ number\ of\ sides\ of\ regular\ polygon:\\\\ interior\angle= 180^\circ-\frac{360^\circ}{n}\\ 170^\circ=180^\circ-\frac{360^\circ}{n}\\ -10^\circ=-\frac{360^\circ}{n}\ |*n\\ -10^\circ\ *n=-360^\circ \ |:-10^\circ\\ n=36\\\\ Number\ of\ sides\ is\ 36.$

You might be interested in

Finding the original price given the sale price and percent...

bulgar [2K]

Answer:

$325

Step-by-step explanation

78% is 234

x is 100%

cross multiply

$\frac{234}{72}$ = $\frac{x}{100}$

234 × 100 = 72x

23400 = 72x

23400÷72 =72x ÷72

325 = x

4 0

3 years ago

Help Nxhxhxhdhdhdbsbsbdhdhd

Annette [7]

Your answer is number 2 it is 38.2 because 26 out of 68 is a percentage of 38.24

3 0

3 years ago

The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per t

lys-0071 [83]

Answer:

The null and alternative hypothesis for this study are:

$H_0: \mu=18500\\\\H_a:\mu< 18500$

The null hypothesis is rejected (P-value=0.004).

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.

Then, the null and alternative hypothesis are:

$H_0: \mu=18500\\\\H_a:\mu< 18500$

The significance level is 0.05.

The sample has a size n=150.

The sample mean is M=18200.

The standard deviation of the population is known and has a value of σ=1400.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31$

Then, we can calculate the z-statistic as:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624$

This test is a left-tailed test, so the P-value for this test is calculated as:

$P-value=P(z$

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.

3 0

3 years ago

A train has 10 cars numbered 1 through 10. If the cars are coupled randomly, what is the probability that the first3 cars are in

Pepsi [2]

You would have a 3 to 10 chance that the first 3 cars are in order

8 0

3 years ago

Read 2 more answers

Which Two Numbers Add Up To Negative 26 And Multiply To 11?

Fynjy0 [20]

Xy=11
x+y=-26

x+y=-26
minus x both sides
y=-26-x

sub for y
x(-26-x)=11
-26x-x^2=11
add 26x+x^2 both sides
x^2+26x+11=0

ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$

a=1
b=26
c=11

x= $\frac{-26+/-\sqrt{26^{2}-4(1)(11)} }{2(1)}$
x= $\frac{-26+/-\sqrt{676-44} }{2}$
x= $\frac{-26+/-\sqrt{632} }{2}$
x= $\frac{-26+/-2\sqrt{158} }{2}$
x= $-13+/-\sqrt{158}$

x= $-13+\sqrt{158}$ or $-13-\sqrt{158}$

aprox

x=-0.420195 or -25.5698

those are the numbers

5 0

3 years ago